Lovren started the Premier League game at Selhurst Park and played for the entire 90 minutes, as the Reds won 2-1 despite going down to 10 men just past the hour mark.
The Croatia international defender took one shot, had a pass accuracy of 82%, created one chance, put in one cross, won 38% of his tackles and 86% of his headers, and made one interception, 10 clearances and two blocks.
Crooks was impressed with the performance of the former Southampton centre-back and included him in his BBC Premier League Team of the Week.
“It has taken quite some time for Dejan Lovren to come to terms with the demands placed on him by Liverpool since his arrival from Southampton,” the Englishman told BBC Sport.
“His performance in Liverpool's 2-1 win against Crystal Palace - particularly with the Reds having gone down to 10 men - was exceptional.
"Just why it's taken Lovren so long to settle in at Anfield isn't clear but he looks like he's finally starting to come to terms with the expectation.”
Lovren joined Liverpool from Premier League rivals Southampton in the summer of 2014, but he has yet to prove himself at Anfield.
The 26-year-old has made some costly mistakes during his time at the Reds, and just like Liverpool, he is inconsistent in his performances.
Lovren was good against Palace, but he needs to maintain this level for the rest of the season.